[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 243 from proof refine-sync (previous step)

# lpt0 = # avol0, # lpt1 = # avol0, # gndx = # lax, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, avol0[pstate.lnum] = mapped(buf), lpt1[pstate.lnum] = mklp(m0, # buf, LP_GROUP_NODES, m7), gstore2[pstate.lnum] = groupblock(gndx, lax, m0), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, n < # buf1, ginval < # avol0, pstate.lnum < # avol0, abs-istore(avol0, lpt1, istore2), abs-nodes(buf, gndx, lax, # buf = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], buffered(pstate.lnum)), awbuf-inv(avol0, buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(gstore2 \ ginval), inv(gstore1), inv(istore2), inv(istore1), inv(groupblock(gndx, lax, m0)), is-aligned(# buf, 2 * NODE_HEADER_SIZE), is-aligned(# buf + n, EB_PAGE_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt0), lpt-free-unref(lpt1), lpt-leb-size(lpt0), lpt-leb-size(lpt1), lpt-ram-flash(lpt1, lpt0, log1), lpt-ram-flash(lpt1[pstate.lnum, mklp(m0, LEB_SIZE, LP_GROUP_NODES, m7)], lpt0, log1), pstate.lnum ∈ gstore2, # buf ≤ LEB_SIZE, # buf + # buf1 ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.index? → pstate.lnum ∈ istore2, pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last, pstate.index? ∨ pstate.journal? ⊦ buf1 = mkbuf(0), n = 0, pstate = unbuffered, pstate = readonly, abs-nodes(buf + subarray(buf1, 0, n), gndx, lax, true), dups(log1), is-aligned(# buf, EB_PAGE_SIZE), pstate.lnum ∈ ginval

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 244:
# gndx = # lax, # lpt1 = # avol0, # lpt0 = # avol0, EB_PAGE_SIZE = # buf1 + # buf % EB_PAGE_SIZE, gstore2[pstate.lnum] = groupblock(gndx, lax, m0), lpt1[pstate.lnum] = mklp(m0, # buf, LP_GROUP_NODES, m7), avol0[pstate.lnum] = mapped(buf), keyset(gch) = gc-heap(lpt1, log1), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems log1 ∩ ginval = ∅, dom gstore1 ∪ elems log1 = dom gstore2 ∪ ginval, pstate.lnum < # avol0, ginval < # avol0, n < # buf1, abs-istore(avol0, lpt1, istore2), abs-nodes(buf, gndx, lax, # buf = LEB_SIZE), abs-padding(buf1), awbuf-inv(avol0, buffered(pstate.lnum)), awbuf-inv(avol0[pstate.lnum, mapped(buf + subarray(buf1, 0, n))], buffered(pstate.lnum)), bin-heap-inv(gch, lpt1), buf-ro-rw-mode(false, buffered(pstate.lnum), lpt1, avol0), bufs-log-only(buffered(pstate.lnum), log1, lpt1), flash-lpt-cons(lpt0, istore1, gstore1), freelist-cons(lpt1, freelist), inv(groupblock(gndx, lax, m0)), inv(istore1), inv(istore2), inv(gstore1), inv(gstore2 \ ginval), is-aligned(# buf + n, EB_PAGE_SIZE), is-aligned(# buf, 2 * NODE_HEADER_SIZE), log-group-block(log1, lpt1), lpt-free-unref(lpt1), lpt-free-unref(lpt0), lpt-leb-size(lpt1), lpt-leb-size(lpt0), lpt-ram-flash(lpt1[pstate.lnum, mklp(m0, LEB_SIZE, LP_GROUP_NODES, m7)], lpt0, log1), lpt-ram-flash(lpt1, lpt0, log1), pstate.lnum ∈ gstore2, # buf + # buf1 ≤ LEB_SIZE, # buf ≤ LEB_SIZE, istore1 ⊑ istore2, ⌊err1⌋ , pstate.journal? → log1 ≠ [] ∧ pstate.lnum = log1.last, pstate.index? → pstate.lnum ∈ istore2, pstate.index? ∨ pstate.journal? ⊦ # buf = LEB_SIZE, buf1 = mkbuf(0), n = 0, pstate = readonly, pstate = unbuffered, abs-nodes(buf + subarray(buf1, 0, n), gndx, lax, true), dups(log1), is-aligned(# buf, EB_PAGE_SIZE), pstate.lnum ∈ ginval

Rule argument

fma: # buf = LEB_SIZE

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ is-aligned(LEB_SIZE, EB_PAGE_SIZE); (ss)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s) Used formulas: # buf = LEB_SIZE